for smooth \(p\)  the integration along a boundary \(\Gamma _t\subset \partial \Omega ^\pm _t\) 
is given by the formula (see e.g. [1]}):
\(\int _{\Gamma _{t}} ( {\rm div}_{\tau _t} \Lambda \, p +\Lambda \cdot \nabla p) \,dS_x=\int _{\Gamma _{t}} (n_t\cdot \Lambda ) ( \varkappa _{t} p +n_t\cdot \nabla p) \,dS_x+{\left\lbrace \begin{array}{ll}(\tau _t\cdot \Lambda ) p|_{\partial \Gamma _{t}}& \text{in 2D,}\\{\displaystyle \int _{\partial \Gamma _{t}}} (b_t\cdot \Lambda ) p \, dL_x & \text{in 3D.}\end{array}\right.}\) 
